# What Are the Final Velocities After a Two-Dimensional Collision?

• hdo
In summary, after the collision between a 6kg object moving at 3m/s and another 6kg object at rest, the first object moved off at a 40 degree angle to the left of its original path while the second object moved to the right of the first object's original path. Using the equations for the x and y direction, the final velocities of both objects can be calculated."
hdo
problem:
before - 1st object: m=6kg, v=3m/s
2nd object: m=6kg, v=0m/s
after - 1st object move off in a direction 40 degree to the left of its original path
2nd move to the right of the first's original path
find the speech of each object after the collision
equations:
x-direction: m1v1ix + m2v2ix = m1v1fx + m2v2fx
y-direction: m1v1iy + m2v2iy = m1v1fy + m2v2fy

Welcome to PF!

Hi hdo! Welcome to PF!:

(try using the X2 tag just above the Reply box )
hdo said:
… 2nd move to the right of the first's original path

Do you mean at 90º?

ok, those are the correct equations … now put the numbers in …

what do you get?

(btw, all the masses are the same, 6 kg, so you can leave them all out! )

Based on the given information, it appears that the two objects have collided in a two-dimensional scenario. This means that the objects have both a horizontal and vertical component to their motion. To determine the final velocities of each object after the collision, we can use the conservation of momentum principle, which states that the total momentum of a system remains constant before and after a collision.

Using the equations provided, we can set up a system of equations to solve for the final velocities. In the x-direction, we have:

m1v1ix + m2v2ix = m1v1fx + m2v2fx
6kg * 3m/s + 6kg * 0m/s = m1v1fx + 6kg * v2fx

Solving for the final velocity of the first object, we get:

m1v1fx = 6kg * 3m/s + 6kg * 0m/s - 6kg * v2fx
m1v1fx = 18kgm/s - 6kgv2fx
v1fx = (18kgm/s - 6kgv2fx) / 6kg
v1fx = 3m/s - v2fx

Similarly, in the y-direction, we have:

m1v1iy + m2v2iy = m1v1fy + m2v2fy
0kg * 3m/s + 6kg * 0m/s = m1v1fy + 6kg * v2fy

Solving for the final velocity of the first object, we get:

m1v1fy = 0kg * 3m/s + 6kg * 0m/s - 6kg * v2fy
m1v1fy = 0kgm/s - 6kgv2fy
v1fy = (0kgm/s - 6kgv2fy) / 6kg
v1fy = -v2fy

Therefore, the final velocities of the two objects are:

Object 1: v1fx = 3m/s - v2fx, v1fy = -v2fy
Object 2: v2fx = v2fx, v2fy = 0m/s

To find the direction of the final velocities, we can use the trigonometric relationship between the angle of motion and

## 1. What is a two-dimensional collision?

A two-dimensional collision is a type of collision that occurs between two objects in a two-dimensional space, such as a flat surface. In this type of collision, the objects involved move in two dimensions, typically referred to as the x and y axes.

## 2. How is momentum conserved in a two-dimensional collision?

Momentum is conserved in a two-dimensional collision by applying the principle of conservation of momentum, which states that the total momentum of a closed system remains constant. In a two-dimensional collision, the total momentum in the x-direction and y-direction must be conserved separately.

## 3. What is the difference between an elastic and inelastic collision in two dimensions?

An elastic collision in two dimensions is one in which the total kinetic energy of the system is conserved. In contrast, an inelastic collision is one in which the total kinetic energy is not conserved, and some of the energy is converted into other forms, such as heat or sound.

## 4. How are the collision angles and velocities calculated in a two-dimensional collision?

In order to calculate the collision angles and velocities in a two-dimensional collision, the principles of conservation of momentum and conservation of kinetic energy are used. These equations, along with the masses and initial velocities of the objects, can be used to solve for the final velocities and angles of the objects after the collision.

## 5. What are some real-world examples of two-dimensional collisions?

Two-dimensional collisions can be observed in many real-world scenarios, such as billiard balls colliding on a pool table, cars colliding at an intersection, or balls hitting each other in a game of sports. These collisions can also be simulated and studied in scientific experiments to better understand the laws of motion and energy conservation.

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